A digital image captured with your camera has a fixed number of sensor sites which record data. The final result of this data are a fixed number of pixels in a horizontal by vertical matrix of a size determined by the sensor receptor site density. Essentially you end up with a number commonly referred to in "megapixels".

When you print, the printer requires a given density referred to in "dpi" (dots per inch) which produces an image of a fixed dimension. Since you want to print your images at a size commonly used to frame or cut such as 4x6 or 5x7 or 8x10, etc., you need a way to alter the actual number of pixels so that the requirements of the printer are satisfied as well as your need for a given sized print.

Rarely do the default size which your capture produces at a given "dpi" and what you want in terms of print size correspond, so you need to either add pixels or remove pixels to make the pixel density correct for the size you want to print. This is where a process called interpolation comes in.

Interpolation software is designed to examine adjacent pixel values (numbers) and actually "create" intermediate values. This is done throughout the image and the result is an image which is larger (because of the added pixels) than the original while maintaining the proper pixel density (how many pixels per unit of measurement) to satisfy the printer's requirements.

The process is generally referred to as "resampling" and this process either removes pixels throughout the image, or adds pixels throughout the image. How many are added or removed depend on the print density selected and the size of the image you want to end up with.

Various different math formulae have been devised to do this "interpolation." They have names like bicubic, spline, Vector, Genuine Fractals, etc. These different approaches result in either an image with sharp edges (fractal interpolation) or smooth edges (bicubic) or something in between. There are numerous methods of doing interpolation. Some are better for one or another type image and depending on how large the final print will be and how well fine detail was captured in the first place.

Obviously, there is much more to this than this brief explanation, but this will get you started on understanding interpolation.

Interpolation = making an image look smoother by graduating between set points of colour.

Enlarged photos naturally look blocky because you can see all the square dots (pixels) that make up the image. Interpolating smoothens out the blockiness by calculating gradiations of colour between all the pixels in the image.

Therefore, interpolation adds no new detail to an image, but it makes it less blocky when you enlarge it.